Talk:Quantum gate

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The article asserts that R(\cos^{-1}\begin{matrix} \frac{3}{5} \end{matrix})) along with a couple of other gates form a "universal" set of gates. What is the significance and/or derivation of 3/5? Would other angles work as well? What is the critical property of the particular angle? --David Battle 01:39, 18 August 2005 (UTC)

The fact that it's usable at all is due to the fact that it divided by 2pi is irrational, I believe. For all irrational numbers x all real numbers r in [0,1) and all open intervals that include r, there is an integer n such that nx mod 1 is in the interval. Why this specific angle? Well, eθi = cosx + isinx, so e^{\cos^{-1}\begin{matrix} \frac{3}{5} \end{matrix}} = \cos (\cos^{-1}\begin{matrix} \frac{3}{5} \end{matrix}) + i \sin (\cos^{-1}\begin{matrix} \frac{3}{5} \end{matrix}), which I believe is \frac{3}{5} + i \frac{4}{5}, whose absolute value is 1. The associated angle (the argument of this number) is irrational--I think. Actually, using ei for that term of the matrix should work as well, and it's pretty simple, too. Now my question is why an angle is being multiplied by 2pi. --Ihope127 23:10, 19 June 2007 (UTC)

[edit] Rotating qubit

Rotating about x axis:

R_x(\frac{2\pi}{n}) = \begin{bmatrix} \cos\frac{\pi}{n} & -i\sin\frac{\pi}{n} \\ -i\sin\frac{\pi}{n} & \cos\frac{\pi}{n} \end{bmatrix} .

Rotating about y axis:

R_y(\frac{2\pi}{n}) = \begin{bmatrix} \cos\frac{\pi}{n} & -\sin\frac{\pi}{n} \\ \sin\frac{\pi}{n} & \cos\frac{\pi}{n} \end{bmatrix} .

Rotating about z axis:

R_z(\frac{2\pi}{n}) = \begin{bmatrix} \cos\frac{\pi}{n}-i\sin\frac{\pi}{n} & 0 \\ 0 & \cos\frac{\pi}{n}+i\sin\frac{\pi}{n} \end{bmatrix} .

http://jquantum.sourceforge.net/jQuantumApplet.html


[edit] Quantum gate (PC game) confusion

concerning articles :1:Quantum gate, 2:Quantum Gate and 3:Quantum Gate (PC game) previously, 3 redirected to 2 which held the info about the game, which i thought was very confusing, as it was clear to me that 2 should redirect to 1, with 3 holding the information about the game, so i moved the game information from 2 to 3, and redirected 2 to one, this will be coppied on the other two articles' talk page 193.60.83.241 (talk) 11:47, 14 May 2008 (UTC)